Many integrated circuit (IC) manufacturers have techniques to authenticate their ICs. For example, some manufacturers may build special circuitry in their ICs for authentication purposes. In some situations, such circuitry may be replicated (e.g., cloned) by reverse engineering. However, variations in fabrication processes usually cause the structure of the replicated circuitry to be slightly different from the original circuitry. Therefore, the function of the replicated circuitry would not be the same as the function of the original circuitry. Thus, most circuitry used for authentication purposes have an inherent physically-unclonable function (PUF). Based on this PUF feature, using PUF circuits for product authentication is favorable for many manufacturers. However, some of these conventional PUF circuits may have constraints that are unsuitable to be built in some products (e.g., ICs). Such constraints may include large circuit area, excessive fabrication process overhead, high power consumption, and high cost.